My utility has these on most people's heaters. It doesn't save you anything, it just lets them shut off your heater when loads are high (typically 5:30-7:30 pm) or there's a large energy hog event (super hot day with everyone's AC running, super cold day when everyone's on emergency heat).
So it's not for energy savings, it's for "grid health" so they don't have to switch on expensive peaking plants.
My provider gives you a one-time $50 bill credit if you let them install it. I declined to participate since I have a
hybrid hot water heater anyway. That saves me about $20-25/month and doesn't use the 4.5kw heating coils regular units do that make them such a potent drain on the grid.